One-point function estimates for loop-erased random walk in three dimensions
Probability
2018-07-03 v1 Mathematical Physics
math.MP
Abstract
In this work, we consider loop-erased random walk (LERW) in three dimensions and give an asymptotic estimate on the one-point function for LERW and the non-intersection probability of LERW and simple random walk in three dimensions for dyadic scales. These estimates will be crucial to the characterization of the convergence of LERW to its scaling limit in natural parametrization. As a step in the proof, we also obtain a coupling of two pairs of LERW and SRW with different starting points conditioned to avoid each other.
Cite
@article{arxiv.1807.00541,
title = {One-point function estimates for loop-erased random walk in three dimensions},
author = {Xinyi Li and Daisuke Shiraishi},
journal= {arXiv preprint arXiv:1807.00541},
year = {2018}
}
Comments
39 pages, 2 figures